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Annotation of OpenXM/src/asir-contrib/testing/taka_series.rr, Revision 1.2

1.2     ! takayama    1: /* $OpenXM: OpenXM/src/asir-contrib/testing/taka_series.rr,v 1.1 2005/05/04 05:47:03 takayama Exp $ */
1.1       takayama    2:
                      3: module tkseries;
                      4:
                      5: localf quote_input_form0$
                      6: localf diff1$
                      7: localf diffn$
                      8: localf expand1$
                      9: localf myeval$
                     10:
                     11: /* Todo */
                     12: /* qt.dtoq, qtod;  quote<-->dp   */
                     13: /* qt.ltoq, qtol;  quote<-->list */
                     14:
                     15: #define O_N 1
                     16: #define O_P 2
                     17: #define O_R 3
                     18: #define O_LIST 4
                     19: #define O_VECT 5
                     20: #define O_MAT 6
                     21: #define O_STR 7
                     22: #define O_COMP 8
                     23: #define O_DP 9
                     24: #define O_USINT 10
                     25: #define O_ERR 11
                     26: #define O_GF2MAT 12
                     27: #define O_MATHCAP 13
                     28: #define O_F 14
                     29: #define O_GFMMAT 15
                     30: #define O_BYTEARRAY 16
                     31: #define O_QUOTE 17
                     32: #define O_OPTLIST 18
                     33: #define O_SYMBOL 19
                     34: #define O_RANGE 20
                     35: #define O_TB 21
                     36: #define O_DPV 22
                     37: #define O_QUOTEARG 23
                     38: #define O_VOID -1
                     39:
                     40: def quote_input_form0(Q) {
                     41:   Q = quotetolist(Q);
                     42:   return quote_input_form_quote_list(Q);
                     43: }
                     44: def diffn(F,X,N) {
                     45:   if ((type(F) == O_LIST) || (type(F) == O_VECT) || (type(F) == O_MAT)) {
                     46:     return map(diffn,F,X,N); /* It will not work for O_MAT */
                     47:   }
                     48:   /* We assume that F is O_QUOTE, O_P or O_R */
                     49:   if (N == 0) return F;
                     50:    for (I=0; I<N; I++) {
                     51:      F = diff1(F,X);
                     52:   }
                     53:   return F;
                     54: }
                     55:
                     56: def diff1(F,X) {
                     57:   if (type(F) == O_QUOTE) {
                     58:      /* It has not yet been implemented. */
                     59:      R = "quote(calc_diff("+quote_input_form0(F)+","+rtostr(X)+"))";
                     60:      return eval_str(R);
                     61:   }
                     62:   /* We assume O_P or O_R */
                     63:   F=diff(F,x);
                     64:   return F;
                     65: }
                     66:
                     67: def myeval(C) {
                     68:   C = objtoquote(C);
                     69:   C = tr.simp_sin(C);  /* It is defined in test1-tr.rr */
                     70:
                     71:   /* Simplifier for quote should be called instead. */
                     72:   if (qt.is_rational(C)) C = eval_quote(C);
                     73:   return objtoquote(C);
                     74: }
                     75:
                     76: /* Series expansion of F at X=C to the degree N */
                     77: def expand1(F,X,C,N) {
                     78:   R = 0;
                     79:   Fn = F;
                     80:   Cn = base_replace(Fn,[[X,C]]);
                     81:   R = tr.simp_zero(R+myeval(Cn));
                     82:   for (I=1; I<=N; I++) {
                     83:      Fn = diff1(Fn,X);
                     84:      Cn = base_replace(Fn,[[X,C]]);
                     85:      Cn = myeval(Cn)/objtoquote(fac(I));
                     86:      Cn = qt.cancel_number(Cn); /* simplify, e.g.,  2/4 --> 1/4 */
                     87:      if (qt.is_minus(Cn)) Cn = qt.add_paren0(Cn); /* -1/2 --> (-1/2) */
                     88:      Po = objtoquote(X-C)^objtoquote(I);
                     89:      R = R + tr.simp_zero(Cn*Po);
                     90:      R = tr.simp_zero(R);
1.2     ! takayama   91:      R = flatten_quote(R,"+");
1.1       takayama   92:   }
                     93:   Rem = eval_str("quote(oO("+rtostr(X)+","+rtostr(N+1)+"))");
1.2     ! takayama   94:   return flatten_quote(R+Rem,"+");
1.1       takayama   95: }
                     96:
                     97:
                     98: endmodule;
                     99:
                    100: /* Screenshot
                    101: [1798] load("tr.rr"); load("taka_series.rr");
                    102: 1
                    103:
                    104: [1874] tkseries.expand1(cos(x),x,0,7);
                    105: quote(1+-1/2*x^2+1/24*x^4+-1/720*x^6+oO(x, 8))
                    106:
                    107: By tr.simp_unary(R),  +- changes to - .
                    108:
                    109: [1875] print_tex_form(@@);
                    110:      1 -  \frac{ 1} { 2}   {x}^{ 2} +  \frac{ 1} { 24}   {x}^{ 4}  -  \frac{ 1} { 720}   {x}^{ 6} + {oO}( {x},  8)
                    111:
                    112: [1876] tkseries.expand1(sin(x),x,0,7);
                    113: quote(1/1*x^1+-1/6*x^3+1/120*x^5+-1/5040*x^7+oO(x, 8))
                    114:
                    115: [1877] print_tex_form(@@);
                    116:       \frac{ 1} { 1}   {x}^{ 1}  -  \frac{ 1} { 6}   {x}^{ 3} +  \frac{ 1} { 120}   {x}^{ 5}  -  \frac{ 1} { 5040}   {x}^{ 7} + {oO}( {x},  8)
                    117:
                    118: */
                    119:
                    120: end$